Suppose $\bf{A}$ is an $m \times n$ matrix of rank $n$ having entries 0s and 1s.
I found that the minimizer of
\begin{align*} {\bf Q}^* = \text{min}_{\bf Q} \ \text{tr}({\bf AQQ}^{T}{\bf A}^{T}) \ \ \text{s.t.} \ {\bf QA = I} \end{align*}
is equivalent to \begin{align*} {\bf Q}^{**} = \text{min}_{\bf Q} \ \text{tr}({\bf QQ}^{T}) \ \ \text{s.t.} \ {\bf QA = I}. \end{align*}
Is it because of objective functions are convex functions of ${\bf Q}$ and $\text{tr}({\bf AQQ}^{T}{\bf A}^{T})$ has a lower bound of $\text{tr}({\bf QQ}^{T})$